While immune memory is a central feature of the immune response of vertebrates, many fundamental questions, such as how long memory will be maintained in the absence of re-stimulation, remain unanswered. The answer to this question is quantitative in nature, and requires the use of mathematical models in addition to experimental research. This grant involves the construction of empirically-based models to address this and other questions on immune memory. Because of the wealth of data available and the need to focus on a soluble set of problems, the grant is limited to the cytotoxic T-cell (CD8+) responses. There are two broad objectives: 1. Quantifying the dynamics of immune cells, In order to keep the theoretical models closely tied to experimental research, one has to accurately quantify the dynamics of immune cells. A theoretical framework to quantify proliferation and death rates of immune cells from the experimental data will be developed. 2. Development of quantitative models for memory and the repertoire. These models will be used to examine the relative contributions of different factors on the maintenance of memory, and to quantitatively estimate the rate of decline of memory in the absence of specific antigen. These models have important implications for vaccination protocols, particularly on the interactions between immune memory to different vaccines. The models will allow us to examine how the rate at which immune memory to one vaccine may decline when other vaccines are administered, and this will be used to suggest improved schedules for vaccination.